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Cosmic topology course

communication

Email.

what

abstract

  • The aim of this course is that the students will gain an elementary intuitive and formal background to understanding the present state of astronomical research about the shape of the Universe. The emphasis will be on observational strategies. General relativity and the details of modern observational cosmology will only be presented very briefly; students who are interested will need to develop deeper understanding through their own reading and other courses.

more details

shape of the Universe

summary of modern cosmology

  • AstroPh:0602280 - George Ellis - Issues in the Philosophy of Cosmology - this is a proper scientific approach, i.e. serious philosophy explained in simple (scientific) words
  • GrQc:9812046 - George Ellis - relativistic cosmology - standard + beyond standard 1998 Cargese notes

online intros to cosmology

wims - wersja online

traditional exercises

intuition building

how

who

  • się dodaj do listy, np Main.PiotrNowak
  • BoudRoukema (lecturer)

exam

  • exam proposal:

the exam itself

  • Final date for lecturer to add new questions to WIMS: Fri 8 May 2026
  • calibration: lecturer should be able to do full exam in 60 minutes with a score of at least 4.5 (out of 5)
  • fixed day/time, expected up to 2 hours, allowed up to 5 hours, at KRA as in a traditional exam; repeat exam possible in September as in official program
  • exam uses a selection of wims exercises made available in exercise mode, i.e. the questions are different but statistically drawn from the same distribution in a multi-dimensional parameter space with N >> 1 parameters
  • same as for exercises: score rounded to nearest number in the set {0, 2, 3, 3.5, 4, 4.5, 5}
  • physics/astro/maths constants: exact: metre-to-second conversion (p129) 1 s = 299792458 m; 1 AU = 149597870700 m; approximate: π \approx 3.14159265359
  • The examination for this subject requires verification that the students are working through examination questions using verifiable tools. Purely online methods of verifying the students' knowledge are insufficient for this course, so a face-to-face "traditional" exam is required. Experience has shown that some students use scientifically invalid methods.

temporary isolated machine

Starting in 2025, the exam will be conducted on a individual computer for each student; the computer will run on a Debian GNU/Linux operating system with no internet connection. This computer will run a (purely local) WIMS server with the statistically same set of exercises as you have available during the semester.
  • differences wrt exercises
    • stronger prerequisite relation between exercises - you must do the easier exercises before being allowed to try the harder ones
    • more severe scoring system: xq instead of xq^{0.3}
    • no internet acccess
    • no access to hand calculators, mobile phones, laptops, or other private computers (mobile phone use OK if you are taking a break away from your screen)
    • fresh shell account - no access to personal notes or scripts; the lecture pdfs will be available in your account
    • you will have the usual FOSS tools: emacs, vim, bash, less, grep, awk, sed, octave, python, numpy, scipy, maxima, gcc, gfortran
    • you will have these files in your guest shell account with md5sums:
      • 47e54ad34928b502b86046f3fda15ddf cosmdist-0.3.12-3ea40c1.tar.gz
      • 757b6cef51acfbd24e5b8d6fcfd2a0c7 Cosmology_30h_lecture.pdf
      • 200b400f0704b6dfb04fef366f98f266 gr_140407.pdf
      • 15b0cb0a9dbc4508277f5513a94290e6 sr_240412.pdf
      • (2026-03-06 TODO: the file version is still TBD) Cosmic_topology.pdf
      • 5a053da1fed410dda159fe7c7a077f72 SI_math_constants
    • physics/astro/maths constants: exact: metre-to-second conversion (p129) 1 s = 299792458 m; 1 AU = 149597870700 m; approximate: π \approx 3.14159265359 - these are given in the file SI_math_constants
    • cheap powerful technology: you may bring in blank paper and some pens/pencils
    • you will need to "register" a new (temporary) account in the WIMS class
    • you will need to show the examiner the "My Score" page when you are satisfied with your grade and ready to have your score written to usosweb.
An example of the software versions is the following, though the actual versions may be more recent: 
$ dpkg -l |awk '{print $1,$2,$3}' |grep -E " (octave|maxima|python3(|-numpy|-scipy)|emacs|vim-tiny|xpdf|evince|gcc|gfortran) "
ii emacs 1:28.2+1-15+deb12u4
ii evince 43.1-2+b1
ii gcc 4:12.2.0-3
ii gfortran 4:12.2.0-3
ii maxima 5.46.0-11
ii octave 7.3.0-2
ii python3 3.11.2-1+b1
ii python3-numpy 1:1.24.2-1+deb12u1
ii python3-scipy 1.10.1-2
ii vim-tiny 2:9.0.1378-2+deb12u2
ii xpdf 3.04+git20220601-1+b2

exercise mode (24/7)

  • exercise mode:
    • Scoring is enabled by default - but this does not count for any official zaliczenie!
    • Scoring is not limited by IP range - you can practice from Spain or Fiji if you wish.
    • anti-LLM-scraper protection (see FAQonLLMs) - ask offline if access to the page https://cosmo.torun.pl/wims is blocked for you
    • link to wims: https://cosmo.torun.pl/wims - the exercise mode sheets have a warning in Polish ,,(bez zaliczenia!)" to remind you that your scores in exercise mode do not count officially
      • Choose Students' area in the left-hand column of the WIMS interface.

5.0 grade points on WIMS - how it's calculated

  • You can get a grade of up to a maximum of 5.0 points from WIMS exercises:
    • 0.0 \le 5 \frac{ \sum_{i=1,n} x_i q_i^{0.3} }{n} \le 5.0 where
      • x_i is the percentage done for a given "sheet" - let us normalise this to the range from 0.0 i 1.0
      • q_i is the "quality" - in the range from 0.0 to 1.0; the power of 0.3 implies that the effect of q_i is weak unless the "quality" parameter is very low
    • how to check your current score:
      • home
        • My scores
          • Global average: something out of 5. Here, something is your total amount of points
  • The formula for a single exercise done m times, is q_m po m razy, gdzie s_1, ..., s_m, which is in the range from 0.0 to 1.0. This is a decaying average, with q_m = \frac{0.85 q_{m-1} + s_m}{1.85}. In other words, the most recent tries at a realisation of an exercise have the most influence on the score for that exercise.
  • Chromium/Chrome bug: As of 2020 to 2024, chromium/chrome browser software has a bug that prevents the display of some of the exercises. Firefox is one browser without the bug. In any case, Chrome is like a two-way mirror with little chance of protecting your privacy (despite EU regulations).
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Topic revision: r2 - 23 Feb 2026, BoudRoukema
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